Reviews

Simon Ings, Daily Telegraph, 22 September 2007:

... One to Nine — ostensibly a simple snapshot of the mathematical world — is a virtuoso stream of consciousness containing everything important there is to say about numbers (and Vaughan Williams, and climate change, and the Pet Shop Boys) in just over 300 pages. It contains multitudes. It is cogent, charming and deeply personal, all at once.

'Dense' does not begin to describe it. There is extraordinary concision at work. Hodges covers colour space and colour perception in two or three pages. The exponential constant e requires four pages. These examples come from the extreme shallow end of the mathematical pool: there are depths here not everyone will fathom. But this is the point: One to Nine makes the unfathomable enticing and gives the reader tremendous motivation to explore further...

...In his dazzling chapter about the number four, Hodges moves within a few pages from Strauss's last songs to to the sizes of notepaper (A4 and the rest) to Fermat's last theorem with such ease that we hardly notice. These and other anecdotes make this the ideal book for everyone interested in the only universal language, especially if their mathematical curiosity exceeds their skill...

You don't have to be a maths whiz to enjoy this book, which gets numbers figured in more ways than you can imagine. Hodges, a mathematician, writes enthusiastially about the magic of numbers and how we can use them to explain things that have previously baffled us. He wanders through the seven deadly sins, the labyrinth of the National Lottery, and even ventures into the realms of computers and Sudoku. And he does it all the while making the experience fun. Numbers play a bigger part in our lives than we realize — Hodges knows that, too, and questions some of our basic assumptions.

No book with the wonderful opening sentence It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife can possibly fail. Though it is a very different work from its classic predecessor, this one should be no exception.

Its content may be characterised as lucid musing, a kind of free association, based on the numbers one to nine. Mathematics and theoretical physics are its main subjects, but it ranges widely through literature, music, philosophy, politics, and whatever else occurs to its author, in a charmingly scholarly and entertaining way. The genre is popular writing about, and popularisation of, mathematics. But the author uses it to display a great range of interests: in mathematics from the very pure to the wholeheartedly applied; in physics from the mundane to the most modern and (to a non-physicist) far-fetched; in music from classical to pop.

A great strength of the book is its power to evoke vast numerical ranges. Physics, for example, deals with the unimaginably tiny numbers associated with quantum-mechanical constants which describe, on a scale developed from human experience, how subatomic particles behave; using that same scale it deals also with the astronomical numbers associated with cosmological theories. Thus the Planck length 10−33cm measures particles, one thousand million million million million million of which, if laid end to end, might just reach across one's fingernail, while the cosmological radius 1028cm is such that ten thousand million million million million fingernails laid side by side would be needed to stretch from here to the end of the world. The one number is 1061 times as large as the other, yet even this is tiny in comparison with some that mathematics can treat and which Dr Hodges helps his readers find delightful ways to comprehend.

Einstein's famous equation E = mc2 relating energy to mass and the (enormous) speed of light is illustrated in several ways: for example, the dust settling every day in a 10 square-metre room, if converted to energy would be comparable with that of the explosion of 1000 tons of TNT or of an earth tremor measuring 4 on the Richter scale; measured in calories it would produce a thousand million of them, enough to feed 400,000 people or power a similar number of light bulbs for the day.

The book is evidence of the author's pride in learning and knowledge, not only his own, but that of the human race. It shows mastery of a huge range of intellectual endeavour. Whether the book can be read so as to transmit any of that learning from writer to reader is perhaps doubtful. There is so much here, and it is treated mostly — though with notable exceptions — at such an impressionistic level, that the reader is unlikely to be able to retain what he or she learns, or acquire that deep understanding which is what real knowledge is. But, although it is sprinkled with charming and well-judged exercises presented as challenges and rated (like Sudoku, which is one of its many leitmotifs) EASY, GENTLE, MODERATE, TRICKY, DIFFICULT, or FIENDISH, the book was never written to be a textbook: it was written to be a joyous read.

And it is a joyous read — mostly. The exceptions are the passages, mercifully rare, where prejudice against school mathematics and, by implication, school teaching of mathematics, strikes a sadly discordant note. Those passages aside, the book can be strongly recommended to all who value C. P. Snow's "two cultures" and the myriads of connections between them.

Apparently, the 'Inner Life of Numbers' encompasses everything from drug dealing (just think of all those fractions) to climate change to our capacity for sight — and yes, sudoku too. Andrew Hodges scoffs at the populist image of mathematicians as 'leading little or no social life' and rightly so, for here is one who clearly loves the world around him. Ingenious, charming and remarkably clear in his explanations, Hodges strides effortlessly along the line between clarification and infantilising. He shows how much the universe relies on the likes of exponentiation, probability theory and prime numbers, while also linking those concepts to our cultural lives. The Department of Education, eternally in search of ways to 'sex up' maths and science, could do worse than adding One to Nine to the curriculum.